The Leviathan number is equal to \(10^{666}! \approx 10^{6.6556570552\times10^{668}}\), where \(n!\) denotes the factorial.[1][2][3]
The number was defined by scientific author Clifford Alan Pickover in 1995. It has been shown to have \(2.5\times10^{665} - 143\) trailing zeros.
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(284\uparrow312\uparrow268\) | \(926\uparrow106\uparrow330\) |
| Down-arrow notation | \(418\downarrow\downarrow256\) | \(299\downarrow\downarrow271\) |
| Steinhaus-Moser Notation | 273[3][3] | 274[3][3] |
| Copy notation | 5[5[669]] | 6[6[669]] |
| H* function | H(221H(221)) | H(222H(221)) |
| Taro's multivariable Ackermann function | A(3,A(3,2220)) | A(3,A(3,2221)) |
| Pound-Star Notation | #*((1))*((8))*12 | #*((1))*((9))*12 |
| BEAF | {284,{312,268}} | {926,{106,330}} |
| Hyper-E notation | E[418]255#2 | E[299]270#2 |
| Bashicu matrix system | (0)(1)[47] | (0)(1)[48] |
| Hyperfactorial array notation | (320!)! | (321!)! |
| Fast-growing hierarchy | \(f_2(f_2(2212))\) | \(f_2(f_2(2213))\) |
| Hardy hierarchy | \(H_{\omega^{22}}(2212)\) | \(H_{\omega^{22}}(2213)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^{26}+\omega6+86}}}(10)\) | \(g_{\omega^{\omega^{\omega^{26}+\omega6+87}}}(10)\) |
See also[]
- Beast number
- Super-leviathan
- Legion's number of the first and second kind
Sources[]
- ↑ Clifford Pickover. Keys to Infinity Wiley. 1995. ISBN 978-0471118572 p.98
- ↑ Leviathan Number from Wolfram MathWorld
- ↑ Notable Properties of Specific Numbers (page 22) at MROB
Specific numbers: Beast number · Belphegor's prime · Legion's number of the first kind · Super-leviathan · Legion's number of the second kind · Leviathan number
Forms of numbers: apocalypse number · apocalyptic number · apocalyptri number · apocalyptetra number · apocalypenta number · apocalyhexakosioihexekontahexa number · Goliath number